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A053605
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Total multiplicity of the eigenvalue 0 in the spectra of the n^(n-2) labeled trees on n vertices.
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0
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1, 0, 3, 8, 135, 1164, 21035, 322832, 7040943, 153153620, 4048737099, 112389077976, 3537768793559, 118535631544316, 4353324736520955, 170245846476629024, 7163230987527864543, 319708454444016133284
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| M. Bauer and O. Golinelli, On the kernel of tree incidence matrices, J. Integer Sequences, Vol. 3 (2000), #00.1.4.
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LINKS
| Bauer-Golinelli paper
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FORMULA
| a_n = n^{n-1}-2 Sum_{2 <= m <= n}(-1)^m n^{n-m}m^{m-2}\binom{n-1}{m-1}
G.f. satisfies x^2+2x-xe^x = Sum_{n >= 1} (a_n/n!) (xe^x e^{-xe^x})^n.
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CROSSREFS
| Sequence in context: A036504 A132491 A083112 * A076147 A132563 A065061
Adjacent sequences: A053602 A053603 A053604 * A053606 A053607 A053608
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Michel Bauer (bauer(AT)spht.saclay.cea.fr), Jan 20 2000
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net), Dec 08 2000
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